Question

Which of the following statement is true?

• A. \( 3 \in \{1, 3, 5\} \)
• B. \( 3 \in \{1, 3, 5\} \)
• C. \( \{3\} \in \{1, 3, 5\} \)
• D. \( \{3,5\} \in \{1, 3, 5\} \)

Hint:

In set theory, \( \in \) denotes "is an element of". Be careful to differentiate between an element of a set and a set itself.

Answer 1

The Correct Option is A

Step 1: Understand the notation. The symbol \( \in \) means "is an element of".
So, when we say \( 3 \in \{1, 3, 5\} \), we are stating that 3 is an element of the set \( \{1, 3, 5\} \). 
Step 2: Analyze the options. 
Option (a): \( 3 \in \{1, 3, 5\} \): This is true because 3 is an element of the set \( \{1, 3, 5\} \).
Option (b): \( 3 \in \{1, 3, 5\} \): This is identical to option (a) and is also true.
Option (c): \( \{3\} \in \{1, 3, 5\} \): This is false because \( \{3\} \) is a set containing 3, not the number 3 itself.
The set \( \{3\} \) is not an element of \( \{1, 3, 5\} \); the number 3 is.
Option (d): \( \{3, 5\} \in \{1, 3, 5\} \): This is false because \( \{3, 5\} \) is a set, and \( \{3, 5\} \) is not an element of the set \( \{1, 3, 5\} \).
The elements of the set \( \{1, 3, 5\} \) are just 1, 3, and 5, not the set \( \{3, 5\} \).
Step 3: Conclusion. 
The correct statement is option (a), which states that 3 is an element of the set \( \{1, 3, 5\} \).